Finite Group Databasebeta

← #24911639

Subgroups — #24911639

Order 10624.

476 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581782C211yesmaximal, characteristic, complemented
2C2×#14581749C211yesmaximal, characteristic
3#19127642C211yesmaximal, characteristic, complemented
4#19127635C211yesmaximal, characteristic, complemented
5#19127627C211yesmaximal, characteristic
6#19127623C211yesmaximal, characteristic
7#19127593C211yesmaximal, characteristic
8#19127590C211yesmaximal, characteristic
9#19127587C211yesmaximal, characteristic, complemented
10#19127585C211yesmaximal, characteristic, complemented
11#19127582C211yesmaximal, characteristic, complemented
12#19127572C211yesmaximal, characteristic
13#19127572C211yesmaximal, characteristic
14C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
15#389×C83C211yesmaximal, characteristic, complemented
16C22×C4×D83C2211yescharacteristic
17#14581782—24no—
18#14581749—24no—
19C2×C4⋊Dic83C2211yescharacteristic
20C2×C4⋊Dic83C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×Dic83⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×C4×Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
35C2×C4×Dic83C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C83⋊#95C2211yescharacteristic
45C83⋊#95C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic
48C2×C4⋊C4×C83C2211yescharacteristic
49C2×C4⋊C4×C83C2211yescharacteristic
50C2×C42×C83C2211yescharacteristic
51#95×C83C2211yescharacteristic
52#95×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C22×Dic83C2311yescharacteristic
55C22×Dic83C2311yescharacteristic
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C2×C4×D83—22no—
62C2×C4×D83—22no—
63C2×C4×D83—22no—
64C4⋊Dic83—22no—
65C4⋊Dic83—22no—
66Dic83⋊C4—22no—
67Dic83⋊C4—22no—
68Dic83⋊C4—22no—
69Dic83⋊C4—22no—
70Dic83⋊C4—22no—
71Dic83⋊C4D414yes—
72(C2×D83)⋊C4—22no—
73(C2×D83)⋊C4—22no—
74(C2×D83)⋊C4—22no—
75(C2×D83)⋊C4—22no—
76(C2×D83)⋊C4—22no—
77(C2×D83)⋊C4—22no—
78C4×Dic83—22no—
79C4×Dic83—22no—
80C4×Dic83—22no—
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C4⋊C4×C83—22no—
89C4⋊C4×C83—22no—
90C4⋊C4×C83—22no—
91C4⋊C4×C83—22no—
92C42×C83—22no—
93C23×C83C2411yescharacteristic
94C22×D83—21no—
95C22×D83—21no—
96C22×D83—21no—
97C22×D83—21no—
98C22×D83—21no—
99C22×D83—21no—
100C22×D83#4112yes—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83C2×D412yes—
120C2×C4×C83#4112yes—
121C2×C4×C83#4112yes—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83C2×D412yes—
141C2×Dic83C2×D412yes—
142C2×Dic83#4112yes—
143C4×D83—28no—
144C22×C83C22×D411yescharacteristic
145C22×C83C2×#4111yescharacteristic
146C22×C83C2×#4111yescharacteristic
147C22×C83C2×#4111yescharacteristic
148C22×C83C2×#4111yescharacteristic
149C22×C832−1+411yescharacteristic
150C22×C832−1+411yescharacteristic
151C2×D83—22no—
152C2×D83—22no—
153C2×D83—22no—
154C2×D83—41no—
155C2×D83—41no—
156C2×D83—41no—
157C2×D83—41no—
158C4×C83—22no—
159C4×C83—22no—
160C4×C83—22no—
161C4×C83—41no—
162C4×C83—41no—
163C4×C83—41no—
164C4×C83—41no—
165Dic83—22no—
166Dic83—22no—
167Dic83—22no—
168Dic83—41no—
169Dic83—41no—
170Dic83—41no—
171Dic83—41no—
172C2×C83#52511yescharacteristic
173C2×C83#52911yescharacteristic
174C2×C83#54111yescharacteristic
175C2×C83#54711yescharacteristic
176C2×C83#54811yescharacteristic
177C2×C83#55211yescharacteristic
178C2×C83#55211yescharacteristic
179D83—42no—
180#2475—831nomaximal, Sylow
181C83#247511yescharacteristic, complemented, Sylow
182C2×#125—831no—
183C2×#117—831no—
184#400—831no—
185#398—831no—
186#397—831no—
187#396—831no—
188#389D8311yescharacteristic, complemented
189#388—831no—
190#388—831no—
191#387—831no—
192#387—831no—
193#387—831no—
194#385—831no—
195#385—831no—
196C4×C4⋊C4—831no—
197C23×C4—831no—
198#125—1664no—
199#117—1664no—
200C2×C4⋊C4—831no—
201C2×C4⋊C4—831no—
202C2×C4⋊C4—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—831no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4C2×D8311yescharacteristic
209C2×C4⋊C4C2×D8311yescharacteristic
210C2×C4⋊C4C2×D8311yescharacteristic
211C2×C4⋊C4C2×D8311yescharacteristic
212C2×C22⋊C4—831no—
213C2×C22⋊C4—831no—
214C2×C22⋊C4—831no—
215C2×C22⋊C4—831no—
216C2×C22⋊C4—831no—
217C2×C22⋊C4—831no—
218C2×C42—831no—
219C2×C42—831no—
220C2×C42—831no—
221C2×C42C2×D8311yescharacteristic
222#95—831no—
223#95—831no—
224#95—831no—
225#95—831no—
226#95—831no—
227#95—831no—
228#95—831no—
229#95—831no—
230#95—831no—
231#95—831no—
232#95C2×D8311yescharacteristic
233#95C2×D8311yescharacteristic
234C24—831no—
235C22×C4—831no—
236C22×C4—831no—
237C22×C4—831no—
238C22×C4—831no—
239C22×C4—831no—
240C22×C4—831no—
241C22×C4—831no—
242C22×C4—1662no—
243C22×C4—1662no—
244C22×C4—1662no—
245C22×C4C22×D8311yescharacteristic
246C22×C4C22×D8311yescharacteristic
247C22×C4C22×D8311yescharacteristic
248C22×C4C22×D8311yescharacteristic
249C22×C4C22×D8311yescharacteristic
250C22×C4C22×D8311yescharacteristic
251C22×C4C22×D8311yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—834no—
257C4⋊C4—1662no—
258C4⋊C4—1662no—
259C4⋊C4—1662no—
260C4⋊C4—1662no—
261C4⋊C4—1662no—
262C4⋊C4—1662no—
263C4⋊C4—1662no—
264C22⋊C4—1662no—
265C22⋊C4—1662no—
266C22⋊C4—1662no—
267C22⋊C4—1662no—
268C22⋊C4—1662no—
269C22⋊C4—1662no—
270C42—22no—
271C42—1662no—
272C42—1662no—
273C42—1662no—
274C23—832no—
275C23—1661no—
276C23—1661no—
277C23—1661no—
278C23—1661no—
279C23—1661no—
280C23—1661no—
281C23C23×D8311yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—832no—
301C2×C4—832no—
302C2×C4—832no—
303C2×C4—1668no—
304C2×C4—1661no—
305C2×C4—1661no—
306C2×C4—1661no—
307C2×C4—1661no—
308C2×C4—1661no—
309C2×C4—1661no—
310C2×C4—1661no—
311C2×C4—1661no—
312C2×C4—1661no—
313C2×C4—1661no—
314C2×C4—1661no—
315C2×C4—1661no—
316C2×C4—1661no—
317C2×C4—1661no—
318C2×C4—1661no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4D4×D8312yes—
323C2×C4#1305058912yes—
324C2×C4#1305059012yes—
325C22—3321no—
326C22—3321no—
327C22—3321no—
328C22—3321no—
329C22—1662no—
330C22—1662no—
331C22—1662no—
332C22C2×D4×D8311yescharacteristic
333C22#41×D8311yescharacteristic
334C22#41×D8311yescharacteristic
335C22C2×#1305058911yescharacteristic
336C22C2×#1305059011yescharacteristic
337C22#1458184011yescharacteristic
338C22#1458184011yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3321no—
347C4—3321no—
348C4—3321no—
349C4—3321no—
350C4—1662no—
351C4—1662no—
352C4—1662no—
353C2—3322no—
354C2#1912821111yescharacteristic
355C2#1912823111yescharacteristic
356C2#1912831211yescharacteristic
357C2#1912835211yescharacteristic
358C2#1912836111yescharacteristic
359C2#1912838311yescharacteristic
360C2#1912839211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#389×C83C2
prime radicalC23×D83C23
hypercenter#389D83
hypocenterC83#2475
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14581782C2semidirect
3. #19127642C2semidirect
4. #19127635C2semidirect
9. #19127587C2semidirect
10. #19127585C2semidirect
11. #19127582C2semidirect
14. C4⋊C4×Dic83C2semidirect
15. #389×C83C2semidirect
181. C83#2475semidirect
188. #389D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145817822
C2×#145817492
#191276422
#191276352
#191276272
#191276232
#191275932
#191275902
#191275872
#191275852
#191275822
#191275722
C4⋊C4×Dic832
#389×C832
#247583